The conventional automatic gearshifting device of the bicycle such as the one disclosed in the U.S. Pat. No. 5,163,881, enables a bicyclist to select an appropriate pedaling gear ratio in accordance with the road conditions so as to maximize the riding effect. In other words, such a conventional automatic gearshifting device is capable of an automatic adjustment of the pedaling gear ratio by means of the centrifugal force of the wheel in motion, in conjunction with a plurality of centrifugal bodies which are linked with a gearshifting mechanism. Such a conventional automatic gearshifting, device as disclosed by the U.S. Pat. No. 5,163,881 is defective in design in that it is rather complicated in construction, and that the centrifugal bodies are susceptible to damage caused by the external force, and further that a rear seat passenger of the bicycle is vulnerable to injury by the centrifugal bodies in motion.